more stats would be good. the general advice is to never fold QQ, 4bet, get it in.
if you believe he has AK/QQ+ only you still have good equity. when you call his 3bet you are looking for save flop: 545r looks save to me, AK missed, right?
there is the chance villain is shoving AK over you. it might be TT/JJ/99 that also wanted a save flop like this. i wouldnt be surprised to see AK as some people cant give up
why are you betting 20 big blinds on the flop and folding? you bet for information? for value? as a bluff? does any of these work?
information betting is stupid, never do it.
for value: if you bet the flop for value, then you have to call. as stated above his range still has AA/KK but sometimes also TT/JJ/AK and the chance of a complete bluff/straight draw etc
as bluff: if you bet as bluff, do you think AA/KK is folding? flop bet: very bad!
he really reps nothing as what would really c-r here that would not bet. he is prob bad given his line as this flop shove folds out all your air and your only calling with the top of your range, which here you folded.
Looks like a badly played KK-AA scared to get out draw on the turn or river, id not be folding this at 50nl or higher
well there is this book called "easy game" and the first chapter is about reasons for betting. there are only 3 and as soon as you realize "why" you bet, it makes much more sense.
3 reason:
value / bluff / collecting dead money
value: obviously get weaker hands to call.
bluff: get stronger hands to fold. think if this is going to happen before you try it!
dead money: if the pot is live, there is no dead money. collecting dead money usually means a cbet like Q9 on A87. its also a bluff. a live pot means when some passive 0.5AF guy starts check/raising you or betting relentlessly: there is no dead money and no way you can bluff